Question

Find the 11th term of the geometric sequence 1, 4, 16, ...

Answer 1

Given series =1,4,16,...

a = 1

r = 4

n = 11

we know that, an = a x r^n-1

a11 = 1 x 4^10

a11 = 1,048,576

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Answer 2

11th term of the geometric sequence = 1048576

Given :

The geometric sequence 1, 4, 16, . . .

To find :

11th term of the geometric sequence

Concept :

For a geometric progression (GP)

$\displaystyle \sf{ }nth \: term \: of \: the \: GP = a \times {r}^{n - 1}$

Where , first term = a and common ratio = r

Solution :

Step 1 of 2 :

Find first term and common ratio

Here the given geometric sequence is 1, 4, 16, . . .

First term = a = 1

Common ratio = r = 4/1 = 4

Step 2 of 2 :

Calculate 11th term of the geometric sequence

11th term of the geometric sequence

$\displaystyle \sf{ = a \times {r}^{11 - 1} }$

$\displaystyle \sf{ = a \times {r}^{10} }$

$\displaystyle \sf{ = 1 \times {4}^{10} }$

$\displaystyle \sf{ = 1048576 }$

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